The fluctuation-dissipation theorem for a non-periodic driver

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In summary, the conversation discusses the fluctuation-dissipation theorem in statistical physics and its objective of predicting dissipated and stored power in a system driven to oscillate about thermodynamic equilibrium. The formulations mentioned assume a sinusoidal driving force, but the question arises of how to determine the fraction of stored energy being dissipated when a monotonic driving force is present, such as in a shearing 'gel' with elasticity. The possibility of measuring this fraction through only monotonic loading is also raised.
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Bavid
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Hi,
I have been trying to understand the fluctuation-dissipation theorem of statistical physics. I understand the objective: to predict the dissipated and stored power in a system driven to oscillate about thermodynamic equilibrium.

Most formulations I have come across assume a sinusoidal driving force.

My question is this: If we have a monotonic driving force, e.g, a shearing 'gel' (that has some elasticity, i.e, there are both storage and dissipation components), how do we decide what fraction of the stored energy is being dissipated? Is it even possible to measure this fraction through only monotonic loading?
 
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Hi,
you mean something like systematically positive external force?
 

FAQ: The fluctuation-dissipation theorem for a non-periodic driver

What is the fluctuation-dissipation theorem for a non-periodic driver?

The fluctuation-dissipation theorem is a fundamental principle in physics that relates the response of a system to an external driving force with the inherent fluctuations of the system. In the case of a non-periodic driver, the theorem states that the ratio of the fluctuations to the response will be the same at all times, even if the driving force is not periodic.

How does the fluctuation-dissipation theorem apply to non-periodic systems?

The fluctuation-dissipation theorem is a general principle that can be applied to any system, regardless of whether the driving force is periodic or not. In non-periodic systems, the theorem states that the fluctuations and response will be proportional to each other, but may not necessarily occur at the same frequency.

Can the fluctuation-dissipation theorem be used to predict the behavior of a non-periodic system?

Yes, the fluctuation-dissipation theorem can be used to predict the behavior of a non-periodic system. By understanding the relationship between fluctuations and response, scientists can make predictions about how a system will respond to an external driving force.

What are some real-world applications of the fluctuation-dissipation theorem for non-periodic drivers?

The fluctuation-dissipation theorem has many applications in various fields, such as biology, chemistry, and engineering. For example, it is used to study the behavior of complex systems like living cells, to understand the dynamics of chemical reactions, and to design efficient electronic devices.

Is the fluctuation-dissipation theorem only applicable to linear systems?

No, the fluctuation-dissipation theorem can be applied to both linear and non-linear systems. However, in non-linear systems, the relationship between fluctuations and response may become more complex, and the theorem may not hold exactly. In these cases, modified versions of the theorem can be used to describe the behavior of the system.

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